Title

Exact Asymptotics of the Optimal Lp-error of Asymmetric Linear Spline Approximation

Department

Mathematics

Document Type

Article

Publication Date

1-2014

Embargo Period

8-31-2017

Abstract

In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space $L_p$, $1\leqslant p\leqslant\infty$, of functions $f\in C^2\left([0,1]^2\right)$ with nonnegative Hessian by piecewise linear splines $s\in S(\triangle_N)$, generated by given triangulations $\triangle_N$ with $N$ elements. We find the exact asymptotic behavior of optimal (over triangulations $\triangle_N$ and splines $s\in S(\triangle_N)$ error of such approximation as $N\to \infty$.

Journal

Jaen Journal on Approximation

Journal ISSN

1889-3066

Volume

6

Issue

1

First Page

1

Last Page

36

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